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2 years ago

5(3x+9)-2x=15x-2(x-5)

Mathematics

1 answer:

Elenna [48]2 years ago

3 0

Answer:

NO solution

Step-by-step explanation:

5(3x+9)−2x=15x−2(x−5)

Step 1: Simplify both sides of the equation.

5(3x+9)−2x=15x−2(x−5)

(5)(3x)+(5)(9)+−2x=15x+(−2)(x)+(−2)(−5)(Distribute)

15x+45+−2x=15x+−2x+10

(15x+−2x)+(45)=(15x+−2x)+(10)(Combine Like Terms)

13x+45=13x+10

Step 2: Subtract 13x from both sides.

13x+45−13x=13x+10−13x

45=10

Step 3: Subtract 45 from both sides.

45−45=10−45

0=−35

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

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2 years ago

The Wilson family invited 100 relatives to their Christmas party. 90 guests had Dutch heritage, 80 had German heritage and 75 ha

nadezda [96]

The answer is 45 i am 100% sure of that!!!

8 0

2 years ago

An education firm measures the high school dropout rate as the percentage of 16 to 24 year olds who are not enrolled in school a

posledela

Answer:

The value of the test statistic $z = -0.6606$

Step-by-step explanation:

From the question we are told that

The high dropout rate is $\mu = 6.1$ % $= 0.061$

The sample size is $n = 1000$

The number of dropouts $x = 56$

The probability of having a dropout in 1000 people $\= x = \frac{56}{1000} = 0.056$

Now setting up Test Hypothesis

Null $H_o : p = 0.061$

Alternative $H_a : p < 0.061$

The Test statistics is mathematically represented as

$z = \frac{\= x - p}{\sqrt{\frac{p(1 -p)}{n} } }$

substituting values

$z = \frac{0.056 - 0.061}{\sqrt{\frac{0.061(1 -0.061)}{1000} } }$

$z = -0.6606$

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2 years ago

Write an indirect proof showing that the diagonals of a parallelogram intersect each other

____ [38]

Its an indirect proof, so 3 steps :-
1) you start with the opposite of wat u need to prove
2) arrive at a contradiction
3) concludeReport · 29/6/2015261
since you wanto prove 'diagonals of a parallelogram bisect each other', you start wid the opposite of above statement, like below :- step1 : Since we want to prove 'diagonals of a parallelogram bisect each other', lets start by assuming the opposite, that the diagonals of parallelogram dont bisect each other.Report · 29/6/2015261

Since, we assumed that the diagonals dont bisect each other,
OC≠OA
OD≠OBReport · 29/6/2015261
Since, OC≠OA, △OAD is not congruent to △OCBReport · 29/6/2015261

∠AOD≅∠BOC as they are vertical angles,
∠OAD≅∠OCB they are alternate interior angles
AD≅BC, by definition of parallelogram
so, by AAS, △OAD is congruent to △OCBReport · 29/6/2015261
But, thats a contradiction as we have previously established that those triangles are congruentReport · 29/6/2015261
step3 :
since we arrived at a contradiction, our assumption is wrong. so, the opposite of our assumption must be correct. so diagonals of parallelogram bisect each other.

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2 years ago

Simplify<br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7B3%7D%7B8%7D%20%7D%20" id="TexFormula1" title=" \sqrt{ \f

Pie

Answer:

B (√6)/4

Step-by-step explanation:

The smallest multiplier that will make the denominator of the fraction into a perfect square is 2, so you have ...

$\displaystyle\sqrt{\frac{3}{8}}=\sqrt{\frac{3\cdot 2}{8\cdot 2}}\\\\=\sqrt{\frac{6}{16}}=\frac{\sqrt{6}}{\sqrt{16}}\\\\=\frac{\sqrt{6}}{4}$

_____

Answer choice D is also a correct rationalization of the denominator, but is not simplified as far as it can be. √24 = 2√6, so a factor of 2 can be cancelled from numerator and denominator, giving answer choice B.

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2 years ago